mbd_scs Module

$$\begin{gathered} \bar\alpha_i=\tfrac13\operatorname{Tr} \big(\textstyle\sum_j\boldsymbol{\bar\alpha}_{ij}\big),\qquad \boldsymbol{\bar\alpha}=(\boldsymbol\alpha^{-1}+\mathbf T_\text{GG})^{-1} \\ \partial\boldsymbol{\bar\alpha}= -\boldsymbol{\bar\alpha}( \partial\boldsymbol\alpha^{-1}+\partial\mathbf T_\text{GG} )\boldsymbol{\bar\alpha},\qquad \frac{\partial\bar\alpha_i}{\partial X_j}= -\frac13\sum_{\zeta\eta}\big( B_{i\zeta,j\eta}\bar\alpha'_{\zeta,j\eta}+ B'_{j\eta,\zeta}\bar\alpha_{j\eta,i\zeta} \big) \\ \mathbf B=\boldsymbol{\bar\alpha}\mathbf A, \quad A_{i\zeta,j\eta}= \frac{\partial(\alpha_i^{-1})}{\partial X_i} \delta_{ij}\delta_{\zeta\eta}+ \frac{\partial T^\text{GG}_{i\zeta,j\eta}}{\partial X_i},\quad \bar\alpha'_{\zeta,p}=\sum_i\bar\alpha_{i\zeta,p},\quad B'_{p,\zeta}=\sum_iB_{p,i\zeta} \end{gathered}$$

Arguments

Return Value real(kind=dp) (size(alpha))